Kim模型下超导圆柱体中的夹杂对裂纹的影响
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摘要
建立一个含有夹杂和中心裂纹的圆柱状YBaCuO超导体的分析模型,将该超导圆柱体置于外磁场中,超导圆柱将受到电磁力作用.通过有限元方法求解裂纹尖端的应力强度因子,求解得到的数值结果可以反映出超导圆柱在电磁力作用下的断裂行为.基于临界态Kim模型,忽略夹杂和裂纹对屏蔽电流的影响,讨论零场冷却过程中裂纹尖端应力强度因子值的变化规律.结果表明,外磁场、夹杂的杨氏模量、夹杂与裂纹的间距、夹杂的半径以及裂纹长度等因素对裂纹有显著影响.
An analysis model of cylindrical YBaCuO superconductor with inclusions and central cracks inside is established. This cylindrical superconductor is placed in external magnetic field and it will be subjected to the action of electromagnetic force. The stress intensity factor at crack tip found with finite element method and its magnitude is able to reflect its fracture behavior. Based on the critical form of Kim model, the variation rule of stress intensity factor at crack tip during zero field cooling is discussed when the influence of inclusions and crack on shielding current is ignored. The result shows that external magnetic field, Young′s modulus of inclusion, inclusion-crack interval inclusion radius, and crack length will have obvious effects on the crack.
An analysis model of cylindrical YBaCuO superconductor with inclusions and central cracks inside is established. This cylindrical superconductor is placed in external magnetic field and it will be subjected to the action of electromagnetic force. The stress intensity factor at crack tip found with finite element method and its magnitude is able to reflect its fracture behavior. Based on the critical form of Kim model, the variation rule of stress intensity factor at crack tip during zero field cooling is discussed when the influence of inclusions and crack on shielding current is ignored. The result shows that external magnetic field, Young′s modulus of inclusion, inclusion-crack interval inclusion radius, and crack length will have obvious effects on the crack.
引文
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[5] XUE F,ZHANG Z,ZENG J,et al.Effect of an elliptical inclusion on critical current density of a long cylindrical high- T,c,superconductor [J].Journal of Superconductivity & Novel Magnetism,2016,29(8):2023-2029.
[6] RU C Q.Effect of interphase layers on thermal stresses within an elliptical inclusion [J].Journal of Applied Physics,1998,84(9):4872-4879.
[7] CENIGA L,DIKO P.Matrix crack formation in Y-Ba-Cu-O superconductor [J].Physica C Superconductivity,2003,385(3):329-336.
[8] WANG X,YONG H,XUE C,et al.Inclined crack problem in a rectangular slab of superconductor under an electromagnetic force [J].Journal of Applied Physics,2013,114(8):24421-24426.
[9] RODRIGUEZ J P,BARNES P N,VARANASI C V.In-field critical current of type-Ⅱ superconductors caused by strain from nanoscale columnar inclusions [J].Physical Review B Condensed Matter,2008,78(5):1-11.
[10] ZENG J,WANG X,WU H,et al.Kim model for flux-pinning-induced stress in a long cylindrical superconductor [J].AIP Advances,2016,6(7):22501-22510.
[11] AOKI Y,SUMIYAMA A,MOTOYAMA G,et al.Origin of high-Tc inclusion in noncentrosymmetric superconductor CePt3Si [J].Journal of the Physical Society of Japan,2011,80(6):134-140.
[12] YONG H D,ZHOU Y H,ZENG J.Crack problem in a long cylindrical superconductor [J].Journal of Applied Physics,2008,104(11):39021-39024.
[13] 雍华东.若干先进电磁材料结构的断裂与稳定性等力学特性的理论研究 [D].兰州:兰州大学,2010.
[14] ZENG J,ZHOU Y H,YONG H D.Fracture behaviors induced by electromagnetic force in a long cylindrical superconductor [J].Journal of Applied Physics,2010,108(3):5771-5778.
[15] ZENG J,YONG H D,ZHOU Y H.Edge-crack problem in a long cylindrical superconductor [J].Journal of Applied Physics,2011,109(9):4481-4484.
[16] XUE F,GOU X F.Crack problem for a bulk superconductor with nonsuperconducting inclusions under an electromagnetic force [J].AIP Advances,2015,5(4):712801-712811.
[17] GAO Z W,KANG Y L,ZHOU Y H.Crack tip shielding and anti-shielding effects of parallel cracks for a superconductor slab under an electromagnetic force [J].Journal of Mechanical Science & Technology,2012,26(2):353-357.
[18] GAO Z W,ZHOU Y H,KANG Y L.Crack-inclusion problem for a long rectangular slab of superconductor under an electromagnetic force [J].Computational Materials Science,2011,50(2):279-282.
[19] XUE F,ZHANG Z,GOU X F.Fracture behavior of an inclined crack interacting with a circular inclusion in a high-TC superconductor under an electromagnetic force [J].AIP Advances,2015,5(11):71411-71419.
[20] 李维学,邱宏斌,戴剑锋,等.碳纳米管复合材料中镁基体裂纹尖端应力强度因子有限元分析 [J].兰州理工大学学报,2017,43(5):162-165.
[21] 俞树荣,吴艳萍,荆炀.表面裂纹的三维模型及应力强度因子计算 [J].兰州理工大学学报,2017,43(1):160-164.
[22] SHIH C F,MORAN B,NAKAMURA T.Energy release rate along a three-dimensional crack front in a thermally stressed body [J].International Journal of Fracture,1986,30(2):79-102.
[2] CUI X M,TAO B W,XIONG J,et al.Effect of annealing time on the structure and properties of YBCO films by the TFA-MOD method [J].Physica C Superconductivity & Its Applications,2005,432(3):147-152.
[3] REN Y,WEINSTEIN R,LIU J,et al.Damage caused by magnetic pressure at high trapped field in quasi-permanent magnets composed of melt-textured YBaCuO superconductor [J].Physica C Superconductivity,1995,251(1/2):15-26.
[4] MURAKAMI M,GOTOH S,FUJIMOTO H,et al.Flux pinning and critical currents in melt processed YBaCuO superconductors [J].Superconductor Science & Technology,1991,4(4):S43-S50.
[5] XUE F,ZHANG Z,ZENG J,et al.Effect of an elliptical inclusion on critical current density of a long cylindrical high- T,c,superconductor [J].Journal of Superconductivity & Novel Magnetism,2016,29(8):2023-2029.
[6] RU C Q.Effect of interphase layers on thermal stresses within an elliptical inclusion [J].Journal of Applied Physics,1998,84(9):4872-4879.
[7] CENIGA L,DIKO P.Matrix crack formation in Y-Ba-Cu-O superconductor [J].Physica C Superconductivity,2003,385(3):329-336.
[8] WANG X,YONG H,XUE C,et al.Inclined crack problem in a rectangular slab of superconductor under an electromagnetic force [J].Journal of Applied Physics,2013,114(8):24421-24426.
[9] RODRIGUEZ J P,BARNES P N,VARANASI C V.In-field critical current of type-Ⅱ superconductors caused by strain from nanoscale columnar inclusions [J].Physical Review B Condensed Matter,2008,78(5):1-11.
[10] ZENG J,WANG X,WU H,et al.Kim model for flux-pinning-induced stress in a long cylindrical superconductor [J].AIP Advances,2016,6(7):22501-22510.
[11] AOKI Y,SUMIYAMA A,MOTOYAMA G,et al.Origin of high-Tc inclusion in noncentrosymmetric superconductor CePt3Si [J].Journal of the Physical Society of Japan,2011,80(6):134-140.
[12] YONG H D,ZHOU Y H,ZENG J.Crack problem in a long cylindrical superconductor [J].Journal of Applied Physics,2008,104(11):39021-39024.
[13] 雍华东.若干先进电磁材料结构的断裂与稳定性等力学特性的理论研究 [D].兰州:兰州大学,2010.
[14] ZENG J,ZHOU Y H,YONG H D.Fracture behaviors induced by electromagnetic force in a long cylindrical superconductor [J].Journal of Applied Physics,2010,108(3):5771-5778.
[15] ZENG J,YONG H D,ZHOU Y H.Edge-crack problem in a long cylindrical superconductor [J].Journal of Applied Physics,2011,109(9):4481-4484.
[16] XUE F,GOU X F.Crack problem for a bulk superconductor with nonsuperconducting inclusions under an electromagnetic force [J].AIP Advances,2015,5(4):712801-712811.
[17] GAO Z W,KANG Y L,ZHOU Y H.Crack tip shielding and anti-shielding effects of parallel cracks for a superconductor slab under an electromagnetic force [J].Journal of Mechanical Science & Technology,2012,26(2):353-357.
[18] GAO Z W,ZHOU Y H,KANG Y L.Crack-inclusion problem for a long rectangular slab of superconductor under an electromagnetic force [J].Computational Materials Science,2011,50(2):279-282.
[19] XUE F,ZHANG Z,GOU X F.Fracture behavior of an inclined crack interacting with a circular inclusion in a high-TC superconductor under an electromagnetic force [J].AIP Advances,2015,5(11):71411-71419.
[20] 李维学,邱宏斌,戴剑锋,等.碳纳米管复合材料中镁基体裂纹尖端应力强度因子有限元分析 [J].兰州理工大学学报,2017,43(5):162-165.
[21] 俞树荣,吴艳萍,荆炀.表面裂纹的三维模型及应力强度因子计算 [J].兰州理工大学学报,2017,43(1):160-164.
[22] SHIH C F,MORAN B,NAKAMURA T.Energy release rate along a three-dimensional crack front in a thermally stressed body [J].International Journal of Fracture,1986,30(2):79-102.